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JEE Main 2021 (26 Feb, Shift 2) · Acceleration Due to Gravity

Acceleration Due to Gravity question from JEE Main 2021 (26 Feb, Shift 2)

Q97JEE Main 2021 · 26 FEB · SHIFT 2Medium

Acceleration Due to Gravity

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA: AB will be x: y. The value of x is ________.

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Numerical answer type. Work it out, then open the answer.

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Answer: 4

  1. C is 3200 km =R2= \frac{R}{2} above B: gC=g(R1.5R)2=4g9g_C = g\left(\frac{R}{1.5R}\right)^2 = \frac{4g}{9}
  2. Inside earth g∝rg \propto r: gA=g OAR=4g9⇒OA=4R9g_A = g\,\frac{OA}{R} = \frac{4g}{9} \Rightarrow OA = \frac{4R}{9}
  3. AB=R−4R9=5R9AB = R - \frac{4R}{9} = \frac{5R}{9}, so OA:AB=4:5OA : AB = 4 : 5
  4. So x=4x = 4.
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